| 図の四角形 |  | において， |  | ， |  |
| のとき |  | の長さを求めよ。 |
【問】
|
 | に正弦定理を適用すると |  | より |  |
| 同様に， |  | に正弦定理を適用すると |  | より |  |
| 次に， |  | に余弦定理を適用すると |
| よって |  | であるから |
 |
 | のときの辺 |  | の対辺 | | の長さ一覧 |
| CASE | α(度) | β(度) | γ(度) | δ(度) | CDの長さ | 近似値 |
| 1 | 30 | 15 | 45 | 75 |  | 0.707107 |
| 2 | 30 | 15 | 45 | 90 |  | 0.876327 |
| 3 | 30 | 15 | 45 | 105 |  | 1.36603 |
| 4 | 30 | 15 | 90 | 30 | | 0.707107 |
| 5 | 30 | 15 | 90 | 45 |  | 0.732051 |
| 6 | 30 | 30 | 30 | 30 |  | 0.5 |
| 7 | 30 | 30 | 30 | 60 |  | 0.763763 |
| 8 | 30 | 30 | 30 | 90 |  | 1.32288 |
| 9 | 30 | 30 | 60 | 30 |  | 0.57735 |
| 10 | 30 | 30 | 60 | 60 | 1 | 1 |
| 11 | 30 | 30 | 90 | 30 | 1 | 1 |
| 12 | 30 | 45 | 45 | 45 |  | 0.816497 |
| 13 | 30 | 45 | 60 | 30 | | 0.707107 |
| 14 | 30 | 60 | 30 | 30 | | 0.57735 |
| 15 | 30 | 60 | 30 | 60 |  | 1.52753 |
| 16 | 30 | 60 | 45 | 15 |  | 0.517638 |
| 17 | 30 | 60 | 45 | 45 |  | 1.23931 |
| 18 | 30 | 60 | 60 | 30 | 1 | 1 |
| 19 | 30 | 75 | 30 | 15 |  | 0.408248 |
| 20 | 30 | 75 | 30 | 30 | | 0.707107 |
| 21 | 30 | 75 | 45 | 15 | | 0.707107 |
| 22 | 30 | 90 | 30 | 15 | | 0.517638 |
| 23 | 30 | 90 | 30 | 30 | 1 | 1 |
| 24 | 45 | 15 | 30 | 15 |  | 0.582509 |
| 25 | 45 | 15 | 30 | 90 |  | 0.940199 |
| 26 | 45 | 15 | 30 | 105 |  | 1.11803 |
| 27 | 45 | 15 | 60 | 60 | | 0.876327 |
| 28 | 45 | 15 | 60 | 75 | 1 | 1 |
| 29 | 45 | 15 | 90 | 30 |  | 1.42685 |
| 30 | 45 | 15 | 90 | 45 |  | 1.41421 |
| 31 | 45 | 30 | 45 | 15 |  | 0.645497 |
| 32 | 45 | 30 | 45 | 45 | | 0.816497 |
| 33 | 45 | 30 | 45 | 75 |  | 1.29099 |
| 34 | 45 | 30 | 60 | 30 |  | 0.912871 |
| 35 | 45 | 30 | 60 | 60 |  | 1.22474 |
| 36 | 45 | 45 | 30 | 15 |  | 0.505948 |
| 37 | 45 | 45 | 30 | 60 |  | 1.08565 |
| 38 | 45 | 45 | 45 | 45 | 1 | 1 |
| 39 | 45 | 45 | 60 | 30 | | 1.23931 |
| 40 | 45 | 60 | 30 | 30 | | 0.707107 |
| 41 | 45 | 60 | 30 | 60 |  | 1.58114 |
| 42 | 45 | 60 | 45 | 15 | 1 | 1 |
| 43 | 45 | 60 | 45 | 45 | | 1.41421 |
| 44 | 45 | 75 | 30 | 15 |  | 0.715518 |
| 45 | 45 | 75 | 30 | 30 | | 0.876327 |
| 46 | 60 | 15 | 45 | 75 |  | 1.08012 |
| 47 | 60 | 15 | 45 | 90 |  | 1.22962 |
| 48 | 60 | 15 | 60 | 60 | | 1.22474 |
| 49 | 60 | 15 | 60 | 75 |  | 1.32964 |
| 50 | 60 | 30 | 30 | 30 | | 0.763763 |
| 51 | 60 | 30 | 30 | 60 | 1 | 1 |
| 52 | 60 | 30 | 30 | 90 | | 1.52753 |
| 53 | 60 | 30 | 45 | 15 | | 0.940199 |
| 54 | 60 | 30 | 45 | 45 | | 1.08565 |
| 55 | 60 | 30 | 45 | 75 |  | 1.50597 |
| 56 | 60 | 30 | 60 | 30 | | 1.52753 |
| 57 | 60 | 30 | 60 | 60 |  | 1.73205 |
| 58 | 60 | 45 | 30 | 15 | | 0.707107 |
| 59 | 60 | 45 | 30 | 60 | | 1.22474 |
| 60 | 60 | 45 | 45 | 45 | | 1.41421 |
| 61 | 60 | 60 | 30 | 30 | 1 | 1 |
| 62 | 60 | 60 | 30 | 60 | | 1.73205 |
| 63 | 90 | 15 | 30 | 15 | | 1.08012 |
| 64 | 90 | 15 | 30 | 90 | | 1.41421 |
| 65 | 90 | 15 | 30 | 105 | | 1.58114 |
| 66 | 90 | 15 | 45 | 75 |  | 1.87083 |
| 67 | 90 | 15 | 45 | 90 | 2 | 2 |
| 68 | 90 | 30 | 30 | 30 | | 1.32288 |
| 69 | 90 | 30 | 30 | 60 | | 1.52753 |
| 70 | 90 | 30 | 30 | 90 | 2 | 2 |
| 番号 | 例題 | CASE | 答 |
| 1 |  | 59 |  |
| 2 |  | 46 |  |
| 3 |  | 59 |  |
| 4 |  |  |